• Journal of the Korean Statistical Society
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• v.20 no.2
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• pp.118-138
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• 1991

Given a random sample of size N(unknown) with density f(x $\theta$), suppose that only n observations which lie outside a region R are recorded. On the basis of n observations, the Bayes estimators of $\theta$ and N are considered and their asymptotic expansions are developed to compare their second order asymptotic properties with those of the maximum likelihood estimators and the Bayes modal estimators. Corrections to bias and median bias of these estimators are made. An example is given to illustrate the results obtained.

• Journal of the Korean Data and Information Science Society
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• v.26 no.6
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• pp.1573-1582
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• 2015

In lifetime data analysis, it is generally known that the lifetimes of test items may not be recorded exactly. There are also situations wherein the withdrawal of items prior to failure is prearranged in order to decrease the time or cost associated with experience. Moreover, it is generally known that more than one cause or risk factor may be present at the same time. Therefore, analysis of censored competing risks data are needed. In this article, we derive the Bayes estimators for the entropy function under the exponential distribution with an unknown scale parameter based on multiply Type II censored competing risks data. The Bayes estimators of entropy function for the exponential distribution with multiply Type II censored competing risks data under the squared error loss function (SELF), precautionary loss function (PLF) and DeGroot loss function (DLF) are provided. Lindley's approximate method is used to compute these estimators.We compare the proposed Bayes estimators in the sense of the mean squared error (MSE) for various multiply Type II censored competing risks data. Finally, a real data set has been analyzed for illustrative purposes.

• Communications for Statistical Applications and Methods
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• v.12 no.1
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• pp.19-27
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• 2005

The present paper obtains Bayes estimators for the probability p(Y

• Communications for Statistical Applications and Methods
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• v.27 no.1
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• pp.47-64
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• 2020

In this paper, we derive some estimators of the scale parameter of the exponentiated half-logistic distribution based on the multiply Type-I hybrid censoring scheme. We assume that the shape parameter λ is known. We obtain the maximum likelihood estimator of the scale parameter σ. The scale parameter is estimated by approximating the given likelihood function using two different Taylor series expansions since the likelihood equation is not explicitly solved. We also obtain Bayes estimators using prior distribution. To obtain the Bayes estimators, we use the squared error loss function and general entropy loss function (shape parameter q = -0.5, 1.0). We also derive interval estimation such as the asymptotic confidence interval, the credible interval, and the highest posterior density interval. Finally, we compare the proposed estimators in the sense of the mean squared error through Monte Carlo simulation. The average length of 95% intervals and the corresponding coverage probability are also obtained.

• Journal of the Korean Data and Information Science Society
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• v.2
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• pp.23-39
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• 1991

The maximum likelihood estimators and Bayes estimators of the parameters and reliability function for the two-parameter Weibull distribution under the type-II progressively censoring schemes are derived when a shape parameter is known and unknown, respectively. Efficiencies for above estimators are also compared each other in terms of the mean square errors, and Bayes risk sensitivities of the Bayes estimators are investigated.

• Journal of the Korean Data and Information Science Society
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• v.6 no.1
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• pp.39-51
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• 1995

This paper deals with the problem of obtaining some Bayes estimators of Rayleigh reliability function in a time censored sampling with incomplete information. Using the priors about a reliability function some Bayes estimators are proposed and studied under squared error loss and Harris loss.

• Journal of the Korean Data and Information Science Society
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• v.8 no.2
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• pp.261-270
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• 1997

This paper is proposed the parametric empirical Bayes(EB) confidence intervals which corrects the deficiencies in the naive EB confidence intervals of the scale parameter in the Weibull distribution under item-censoring scheme. In this case, the bootstrap EB confidence intervals are obtained by the parametric bootstrap introduced by Laird and Louis(1987). The comparisons among the bootstrap and the naive EB confidence intervals through Monte Carlo study are also presented.

• Journal of the Korean Data and Information Science Society
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• v.8 no.1
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• pp.31-39
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• 1997

we shall propose some Bayes estimators and some generalized maximum likelihood estimators for reliability of a two-unit hot standby system with perfect switch based upon a complete sample of failure times observed from the exponential model and compare the peformances of the proposed estimators in terms of mean squared error.

• Communications for Statistical Applications and Methods
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• v.3 no.2
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• pp.205-216
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• 1996

Consider the problem of estimating a multivariate normal mean with an unknown covarience matrix under a weighted sum of squared error losses. We first provide hierarchical Bayes estimators which shrink the usual (maximum liklihood, uniformly minimum variance unbiased) estimator towards a regression surface and then prove the admissibility of these estimators using Blyth's (1951) method.

• Journal of the Korean Statistical Society
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• v.30 no.3
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• pp.481-498
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• 2001

Empirical Bayes procedure of nonparametric estiamtion of cumulative hazard rates based on censored data is considered using the beta process priors of Hjort(1990). Beta process priors with unknown parameters are used for cumulative hazard rates. Empirical Bayes estimators are suggested and asymptotic optimality is proved. Our result generalizes that of Susarla and Van Ryzin(1978) in the sensor that (i) the cumulative hazard rate induced by a Dirichlet process is a beta process, (ii) our empirical Bayes estimator does not depend on the censoring distribution while that of Susarla and Van Ryzin(1978) does, (iii) a class of estimators of the hyperprameters is suggested in the prior distribution which is assumed known in advance in Susarla and Van Ryzin(1978). This extension makes the proposed empirical Bayes procedure more applicable to real dta sets.